For metrics that are at least C1,1 maximizing curves must be solutions of the geodesic equation
and hence cannot change causal character: they must remain either timelike or null. This is no
longer obvious for metrics of lower regularity and once the regularity drops below Lipschitz
there are examples of "bubbling" metrics, for which maximizing causal curves may contain
both timelike and null segments. We will present a recent result stating that Lipschitz
regularity of the metric is sufficient for maximizing curves to have fixed causal character
and show how this almost immediately gives a Lipschitz inextendibility result for timelike
geodesically complete spacteimes. This is joint work with E. Ling.
Melanie Graf (Vienna): Low regularity Lorentzian metrics and the causal character of maximizers
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- MelanieGraf_08.03.2018.pdf 120 KB
